If A is a square matrix of order 3, then find $| (A - A^{T})^{2011} |$ .

Open in App

Solution

$G i v e n A i s a s q u a r e m a t r i x o f o r d e r 3 {(A - A^{T})}^{T} = A^{T} - {(A^{T})}^{T} = - (A - A^{T}) i . e A - A^{T} i s a s k e w - s y m m e t r i c m a t r i x \Rightarrow ∣ ∣ A - A^{T} ∣ ∣ = 0 ∣ ∣ {(A - A^{T})}^{2011} ∣ ∣ = {(∣ ∣ A - A^{T} ∣ ∣)}^{2011} = 0$

Suggest Corrections

Similar questions

A

3

| A | = 5

| a d j A |

3

| \begin{matrix} (A d j A) \end{matrix} | =

∣ ∣ \begin{matrix} A d j (A d j A^{2}) \end{matrix} ∣ ∣ =

A

3 \times 3

| A | = 5

| 4 A |

Join BYJU'S Learning Program